How does that Bitcoin mining is safe?

Mining creates the equivalent of a lottery competitive it is extremely difficult for anyone to add new buildings consecutive transactions in the chain of blocks. This protects network neutrality by preventing an individual to have enough power to block certain transactions. It also prevents the situation where someone is trying to replace parts of the chain blocks to reverse its own costs, which could be used to defraud others. Mining makes reversing a transaction prior exponentially worse by the fact that it requires rewriting all the blocks following after that transaction.